evolution of the equilibrium structure of dark matter halos that result from the grav- ... mation from Gaussian-random-noise density fluctuations in a cold dark ...
The Evolution of Dark-Matter Dominated Cosmological Halos
arXiv:astro-ph/0104007v1 2 Apr 2001
Marcelo Alvarez∗ , Paul R. Shapiro∗ and Hugo Martel∗ ∗
Department of Astronomy, University of Texas, Austin, TX 78712
Abstract. Adaptive SPH and N-body simulations were carried out to study the evolution of the equilibrium structure of dark matter halos that result from the gravitational instability and fragmentation of cosmological pancakes. Such halos resemble those formed by hierarchical clustering from realistic initial conditions in a CDM universe and, therefore, serve as a test-bed model for studying halo dynamics. The dark matter density profile is close to the universal halo profile identified previously from N-body simulations of structure formation in CDM, with a total mass and concentration parameter which grow linearly with scale factor a. When gas is included, this concentration parameter is slightly larger than the pure N-body result. We also find that the dark matter velocity distribution is less isotropic and more radial than found by N-body simulations of CDM.
CDM Simulations vs. Observed Halos N-body simulations of structure formation from Gaussian-random-noise density fluctuations in a cold dark matter (CDM) universe have revealed that dark matter halos possess a universal density profile that diverges as r −γ near the center, with 1 ≤ γ ≤ 2 [6] [7]. There exists a discrepancy between these singular density profiles found in N-body simulations and current observations of the rotation curves of nearby dwarf galaxies [6] and of strong lensing of background galaxies by the galaxy cluster CL0024+1654 [10] [8], which suggest that dark-matter dominated halos of all scales have flat density cores, instead. Halo Formation by Pancake Instability and Fragmentation The model we use to examine the formation of dark-matter dominated halos is that of cosmological pancake instability and fragmentation, previously discussed in detail by [12]. Halos formed by such a pancake instability have density profiles very similar to those formed hierarchically in CDM models (e.g. NFW profile [7]), providing a convenient alternative to more complicated simulations with more realistic initial conditions [1] [5] [11]. The ASPH/P3 M simulations considered here were described by [1]; this paper extends that analysis to evolutionary trends in the dark matter halo structure.
FIGURE 1. (left) Dark matter density field at a/ac = 3. (middle) Density profile of the dark matter halo as simulated without gas at four different scale factors, a/ac = 3 (solid), 4 (dotted), 5 (short dash), and 7 (long dash). Shown above are fractional deviations (ρN F W − ρ)/ρN F W from best-fit NFW profile for each epoch. (right) Same as middle, but for DM halo simulated with gas+DM.
Main Results: • For a/ac between 3 and 7, the halo can be fit by an NFW profile, with mass within r200 growing linearly with scale factor a, when simulated either with or without gas: M200 (x) ≃ 0.07x, where x ≡ a/ac , and ac is the scale factor at primary pancake collapse (see Figs. 1 & 2). This mass evolution resembles that of self-similar spherical infall [2], despite the anisotropy associated with pancake collapse and filamentation and periodic boundary conditions. • After a/ac = 3, the concentration parameter cN F W ≡ r200 /rs , determined by best-fitting an NFW density profile [7] to our simulation halos, grows roughly linearly with scale factor a: cN F W (x) ≃ 1.33x−0.18 (without gas), cN F W (x) ≃ 1.49x − 0.37 (with gas) (i.e. the linear slope is steeper in the case with gas included). Fluctuations in cN F W around this trend are smaller when gas is included. This evolution we find for cN F W is reminiscent of that reported for halos in CDM N-body simulations [3]. However, the latter applies to halos of a given mass which are observed at different epochs, and, therefore, reflects the statistical correlation of halo mass with collapse epoch in the CDM model, while our result follows an individual halo. • The anisotropy parameter β ≡ 1 − hvt2 i/(2hvr2 i), where vt (vr ) are tangential (radial) velocities, is shown in Figure 2. Pancake halos are somewhat radially biased, with β ≥ 0.6, about twice the value reported for halos in CDM N-body simulations [4] [9]. With no gas included, the average anisotropy in the halo does not change very much with time, while the inclusion of gas leads to a slight drop after a/ac = 5.
FIGURE 2. (left) Evolution of halo dark matter integrated mass MX as simulated with (dotted) and without (solid) gas, within spheres of average overdensity X ≡ hρi/ρ¯ (in computational units, where Mbox = λ3p ρ¯ = 1). (middle) Evolution of halo concentration parameter for the dark matter halo as simulated with (dotted) and without (solid) gas. (right) Anisotropy parameter β averaged over all dark matter halo particles within a sphere of average overdensity 200, as simulated with (dotted) and without (solid) gas.
This work was supported by NASA ATP grants NAG5-7363 and NAG5-7821, NSF grant ASC-9504046, and Texas Advanced Research Program grant 3658-06241999.
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